A horizontal circular platform rotates counterclockwise about its axis at the ra

Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.963 rad/s. You, with a mass of 73.3 kg, walk clockwise around the platform along its edge at the speed of 1.11 m/s with respect to the platform. Your 20.7-kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 17.9-kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 90.9 kg and radius 1.91 m. Calculate the total angular momentum of the system.

Explanation / Answer

angular momentum of platform L1 = (1/2)*M*R^2*w

L1 = +(1/2)*90.9*1.91*1.91*0.963 = +159.671317635 kg m^2 /s

v1 = v + Rw = (-1.11)+(0.963*1.91) = + 0.72933 m/s

angular momentum of person L2 = m*v1*R

L2 = +73.3*0.72933*1.91 = +102.10838799 kg m^2 /s

v2 = v + Rw/2 = -(1.11/2)+((1.91*0.963)/2) = + 0.364665

m/s

angular momentum of poodle L3 = m*v2**R/2

L3 = +20.7*(0.364665)*(1.91/2) = +7.20888 kg m^2 /s

angular momentum of mutt L4 = I2*w = m*(3R/4)^2*w

L4 = +17.9*(1.4325*1.4325*0.963) = +35.37273 kg m^2 /s

Ltot = L1 L2 + L3 + L4 = +159.671317635 +102.10838799 + 7.20888 +35.37273 = +304.361315625 kg m^2/s

counter clock wise direction

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